Department of Mathematics The Department of Mathematics is a world class leader in mathematical research, education and outreach, and is the top-ranked mathematics department in the United States. It is unique among elite departments in its dedication to teaching and mentoring, and the scope of its program is a key part of MIT’s educational mission at all levels. Our graduates are sought after, both in industry as highly trained problem solvers, and in academics as young researchers. Key to the department’s success is recruitment of the very best junior and senior faculty and graduate students in an ever-more competitive environment. The department strives for diversity in all its appointment and admission levels, and is committed to fostering greater diversity in earlier grades through its numerous outreach programs to high school and middle school students. Our award-winning faculty are leaders working in many central fields in pure and applied mathematics and statistics. We have specialists in analysis, geometry, topology, algebra, and number theory; physical applied mathematics, computational science, computational biology, theoretical computer science (including quantum computing, optimization, machine learning, and computational complexity), combinatorics, probability, and statistics. Because of the department’s breadth, our faculty interact with researchers in other MIT departments, including the Departments of Electrical Engineering and Computer Science; Biology; Physics; Mechanical Engineering; Civil and Environmental Engineering; the Institute for Data, Systems, and Society; as well as the Broad institute. Awards and Honors The faculty received numerous distinctions this year. Professor Frank Thomson Leighton was inducted into the National Inventors Hall of Fame for the content delivery network methods he invented with his graduate student Daniel Lewin. Professor Scott Sheffield and former Schramm and National Science Foundation (NSF) Fellow Jason P. Miller received the 2017 Clay Research Award for their work on the geometry of the Gaussian free field and its application to the solution of open problems in the theory of two-dimensional random structures. Professor Sheffield was also selected for a 2016 Aisenstadt Chair from the University of Montreal. Professor Bonnie Berger was appointed the next Simons Professor of Mathematics. Professor Tobias Colding was awarded the Carlsberg Foundation Research Prize for ground-breaking research in differential geometry and geometric analysis, and Professor Gigliola Staffilani received the 2017 Guggenheim Fellowship. Professors Tomasz Mrowka, Colding, and Staffilani received the 2017 Simons Fellowship. Professor Hung Cheng was honored with the 2017 Distinguished Achievement Award in Technology and Humanity/Humanities by the Chinese Institute of Engineers, San Francisco Bay Chapter. Professor Paul Seidel was appointed distinguished visiting professor at the Institute for Advanced Study for the academic year. Professors David Jerison and Gigliola Staffilani, with Postdoctoral Associate Jennifer French and MITx MIT Reports to the President 2016–2017 1 Department of Mathematics Fellow Karene Chu, made up one of three groups that received the inaugural MITx Prize for Teaching and Learning in MOOCs (massive open online courses). Among the department’s assistant professors, Professor Ankur Moitra received the Packard Fellowship in Science and Engineering. He was also appointed the Rockwell International Career Development Assistant Professor of Mathematics. Professsor Jörn Dunkel was recognized as a 2017 Outstanding Referee by the American Physical Society. Professors Semyon Dyatlov and Aaron Pixton each received a Sloan Research Fellowship. Two faculty members, Professors Vadim Gorin and Philippe Rigollet, were selected by the MIT research support committee for support from the NEC Corporation Fund for Research in Computers and Communication for AY2017. CLE Moore Instructor Roger Casals received the Vicent Caselles Mathematical Research Award of the Banco Bilbao Vizcaya Argentaria (BBVA) Foundation and the Royal Spanish Mathematical Society (RSME). He also received the RSME’s José Luis Rubio de Francia Award and the BBVA Research Fellowship. Lectures John Bush delivered a Sectional Lecture in Fluid Dynamics at the 24th International Congress of Theoretical and Applied Mechanics in Montreal, August 2016. Tobias Colding gave a one-hour American Mathematical Society (AMS) invited address at the Joint Mathematics Meetings in Atlanta, GA, in January 2017. David Jerison presented the Zhu Kezhen Distinguished Lectures at Zhejiang University, Hangzhou, China, in January 2017. William Minicozzi gave the 2017 Ritt Lectures at Columbia University in March 2017. He also gave a talk at the 2016 Clay Research Conference and Workshops at Oxford University, UK, in September 2016. Scott Sheffield presented the Aisenstadt Chair Lectures at the Center for Mathematical Research at the University of Montreal in September 2016. In July 2016, he gave the Doob Lecture at the World Congress of Probability and Statistics at the Fields Institute for Research in Mathematical Sciences in Toronto, and he was a Saint-Flour summer school lecturer in Auvergne, France. Peter Shor delivered the Viterbi Lecture in the Department of Electrical Engineering at the University of Southern California in March 2017. Gigliola Staffilani gave a one-hour AMS invited address at the Joint Mathematics Meetings in Atlanta, GA, in January 2017. Gilbert Strang delivered the Alan Tayler Lecture at Oxford University in November 2016. MIT Reports to the President 2016–2017 2 Department of Mathematics David Vogan gave two of the 18th Takagi Lectures at the University of Tokyo in November 2016. New Faculty and Promotions Elchanan Mossel joined the department faculty as full professor with a joint appointment in the MIT Institute for Data, Systems, and Society. He comes from the University of California, Berkeley, where he was professor of statistics and computer science. Since 2014 he was also professor of statistics at the Wharton School, University of Pennsylvania, on leave from Berkeley. Professor Mossel works in applied probability whose program strongly impacts statistics. His research has resolved open problems in computational biology, machine learning, social choice theory, and economics. One of his projects led to the proof of the “Majority is Stablest” conjecture and confirmed the optimality of the Goemans-Williamson MAX-CUT algorithm. Professor Mossel received his PhD from Hebrew University in 2000 studying under Yuval Peres. Before joining the faculty at UC Berkeley in 2003, he was a fellow at the Microsoft Theory Group and a Miller Research Fellow. Andrew Lawrie joined the faculty as assistant professor from the University of California, Berkeley, where he was an NSF Fellow and member of the Mathematical Sciences Research Institute. Professor Lawrie is an analyst. His program focuses on the asymptotic dynamics of solutions to various geometric dispersive equations, such as the wave map equation. He received his PhD from the University of Chicago in 2013 studying under Wilhelm Schlag. Associate Professor Philippe Rigollet was awarded tenure. Assistant Professor Jared Speck was promoted to associate professor without tenure. Assistant Professor Gonçalo Tabuada was promoted to associate professor without tenure. In Memoriam Bertram Kostant Bertram Kostant, professor emeritus of mathematics at MIT, died at the Hebrew Senior Rehabilitation Center in Roslindale, MA, on February 2, 2017, at the age of 88. Professor Kostant joined the mathematics faculty at MIT in 1962. His field asw in group representations and Lie theory. In the early 1960s he began to develop the method of co-adjoint orbits and geometric quantization, relating symplectic geometry to infinite-dimensional representation theory. Geometric quantization provides a ayw to pass between the geometric pictures of Hamiltonian mechanics and the Hilbert spaces of quantum mechanics. In the early 1960s Kostant proved a purely algebraic result about tridiagonal matrices. In the 1970s he used that result and the ideas of geometric quantization to study Whittaker models (which are at the core of the theory of automorphic forms), and the Toda lattice (a widely studied model for one-dimensional crystals). Kostant’s work ultimately touched almost every corner of Lie theory: algebraic MIT Reports to the President 2016–2017 3 Department of Mathematics groups and invariant theory, the geometry of homogeneous spaces, representation theory, geometric quantization and symplectic geometry, Lie algebra cohomology, and Hamiltonian mechanics. Over the years he supervised more than 20 PhD students, among them the differential geometer James Simons, and served as a mentor to many postdoctoral researchers and young faculty members. He worked with great energy and success to build MIT’s faculty in Lie theory and representation theory. Professor Kostant retired from MIT in 1993 but maintained his very active life in research, travel, and lecturing at universities and conferences around the world. He continued as an active participant in the department’s weekly seminars in Lie theory. Kostant received many awards and honors. He was a 1959–1960 Guggenheim Fellow and a 1961–1963 Sloan Fellow. He was elected to the American Academy of Arts and Sciences in 1962 and to the National Academy of Sciences in 1978. He was awarded the 1990 Steele Prize of the American Mathematical Society in recognition